Shenelle has $100$ meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width $x$ (in meters) is modeled by: $A(x)=-(x-25)^2+625$ What side width will produce the maximum garden area?
The garden's area is modeled by a quadratic function, whose graph is a parabola. The maximum area is reached at the vertex. So in order to find when that happens, we need to find the vertex's $x$ -coordinate. The function $A(x)$ is given in vertex form. The vertex of $-(x-{25})^2{+625}$ is at $({25},{625})$. In conclusion, the maximum area occurs when the rectangle width is $25$ meters.